Minefield method to generating function approximations

[Ravenwater]

John Gustafson's Minefield method to generate perfectly rounded polynomial approximations to mathematical functions could be a powerful solution to the table maker's dilemma.

Santos Nagarakatta and Jay Lim at Rutger's have put together a linear programming model to automatically generate math libraries, presented in this paper:

A Novel Approach to Generate Correctly Rounded Math Libraries for New Floating Point Representations

The complexity of the linear program and the impact on feasibility of selecting the ride argument reduction techniques are domains we need to improve. My litmus test is how one could use these techniques to generate math libraries for 256-bit posits, and we are far from solving that problem.

What do folks think about where the biggest gains can be had:

1. in the argument reduction, or
2. in the linear program articulation?